Let f:(-1,1) r be a differentiable function. which one of the following is necessarily true? (a) if f'(0) >0, then f(r) > f0) for all a e (0,1). (b)if f'0) <0,

Let f:(-1,1) R be a differentiable function. Which one of the following is necessarily true? (a) If f'(0) >0, then f(r) > f0) for all a e (0,1). (b)If f'0) <0, then f(a) < f0) for all a e (0,8) for some >0. )If f'(0)-0, then f(e)- f0) for all a € (-6,6) for some 6 >0. (d) If f0)>0, then f(0)>0. Outians